On the spherically symmetric Einstein-Yang-Mills-Higgs equations in Bondi coordinates

We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christodoulou and D. Chae concerning global solutions for the Einstein-scalar field and the Einstein-Maxwell-Higgs equations. The novelty of the present work is twofold. For one thing the assumption on the self-interaction potential is improved. For another thing explanation is furnished why the solutions obtained here and those proved by Chae for the Einstein-Maxwell-Higgs decay more slowly than those established by Christodoulou in the case of self-gravitating scalar fields. Actually this latter phenomenon stems from the non-vanishing local charge in Einstein-Maxwell-Higgs and Einstein-Yang-Mills-Higgs models.Comment: 25 page

On global well-posedness for the Einstein-Maxwell-Euler system in Bondi coordinates

Weanalyze the Einstein-Maxwell equations for an irrotational stiff fluid. Under the spherical symmetry assumption on the space-time, in Bondi coordinates, the considered model is reduced to a nonlinear evolution system of partial integrodifferential equations. Assuming regularity at the center of symmetry and that the matter content of the initial light cone is the so-called null dust, the characteristic initial value problem associated to the obtained system is solved globally by a contraction mapping argument. In future work we will address the issue of global well-posedness for the considered model in other physically interesting cases where the matter content of the initial light cone is not the null dust.University of Pretoria and a Focus Area Grant from the National Research Foundation of South Africa.http://rendiconti.math.unipd.it/hb201

Avian–human influenza epidemic model with diffusion, nonlocal delay and spatial homogeneous environment

In this paper, an avian–human influenza epidemic model with diffusion, nonlocal delay and spatial homogeneous environment is investigated. This model describes the transmission of avian influenza among poultry, humans and environment. The behavior of positive solutions to a reaction–diffusion system with homogeneous Neumann boundary conditions is investigated. By means of linearization method and spectral analysis the local asymptotical stability is established. The global asymptotical stability for the poultry sub-system is studied by spectral analysis and by using a Lyapunov functional. For the full system, the global stability of the disease-free equilibrium is studied using the comparison Theorem for parabolic equations. Our result shows that the disease-free equilibrium is globally asymptotically stable, whenever the contact rate for the susceptible poultry is small. This suggests that the best policy to prevent the occurrence of an epidemic is not only to exterminate the asymptomatic poultry but also to reduce the contact rate between susceptible humans and the poultry environment. Numerical simulations are presented to illustrate the main results.http://www.elsevier.com/locate/nonrwahj2023Mathematics and Applied Mathematic

A pattern growth-based sequential pattern mining algorithm called prefixSuffixSpan

Sequential pattern mining is an important data mining problem widely addressed by the data mining community, with a very large field of applications. The sequence pattern mining aims at extracting a set of attributes, shared across time among a large number of objects in a given database. The work presented in this paper is directed towards the general theoretical foundations of the pattern-growth approach. It helps indepth understanding of the pattern-growth approach, current status of provided solutions, and direction of research in this area. In this paper, this study is carried out on a particular class of pattern-growth algorithms for which patterns are grown by making grow either the current pattern prefix or the current pattern suffix from the same position at each growth-step. This study leads to a new algorithm called prefixSuffixSpan. Its correctness is proven and experimentations are performed

Efficient mining of intra-periodic frequent sequences

Frequent Sequence Mining (FSM) is a fundamental task in data mining. Although FSM algorithms extract frequent patterns, they cannot discover patterns that periodically appear in the data. However, periodic trends are found in many areas such as market basket analysis, where discovering itemsets periodically purchased by customers can help understand periodic customer behavior. This is the task of Periodic Frequent Pattern Mining (PFPM). A major limitation common to traditional PFPM algorithms is that they reduce the periodicity between non-disjoint itemsets. They do not take into account the periods between disjoint itemsets. Thus, they find itemsets that appear periodically, but would fail to find a periodic appearance of distinct itemsets. To address this limitation, this paper extends the traditional problem of FSM with intra-periodicity and provides a theoretical background to extract intra-periodic frequent sequences. This leads to a new mining algorithm called Intra-Periodic Frequent Sequence Miner. Experimental results confirm its efficiency